Answer to Question #249745 in Microeconomics for sharia

Question

 Rama consumes two goods x and y. Her income is Rs. 1000, x and y are available at a price of Rs. 4 and Rs. 5 per unit respectively. Her utility function is u = xy. (i) Draw her budget line. In the same diagram, shade her new budget set if a tax of Rs.1 per unit is imposed on the consumption of x exceeding 50 units along with an upper limit of 200 units on the consumption of x. Label all important points along with their respective coordinates. (ii) Find her optimum consumption bundle in her new budget set situation

Answer 1

i

Budget equation is represented as

$M=P_X.X+P_Y.Y\implies M=P_1X+P_2Y\\1000=4X+5Y$

$4X+5Y=1000......$ This is the budget line.

After tax imposition on consumption of X

New budget line is set

$(P_1+t)X+P_2Y=M\\P_2Y=M-(P_1+t)X\\Y=\frac{M}{P_2}-\frac{-(P_1+t)X}{P_2}$

A quantity of the tax of Rs.1 per unit of consumption of X. It changes the price of good X from$P_1 \space to\space P_1+1$

$(P_1+1)X+P_2Y=M\\(4+1)X+5Y=M\\5X+5Y=1000.......$ This is the new budget line after tax.

ii

Optimal consumption bundle in the newly set budget situation ;

$IC=-MRS_{XY}=\frac{-MU_X}{MU_Y}\\slope\space of\space U=XY\\MU_X=Y\\MU_Y=X$

slope of $IC=\frac{-Y}{X}$

slope of budget line

$=\frac{-P_X}{P_Y}\\=\frac{-5}{5}=-1$

X=Y

Budget constarint

$\implies5X+5Y=1000\\5X+5Y=1000$

$10Y=1000\\Y=100\\and\\X=Y=100$

therfore optimal consumption bundle (X,Y)=(100,100) in her new budget set situation.